Motion Characteristics for Circular Motion (A-E) A - Circular Motion and Speed
Circular Motion has many different forms. Consisting of uniform constant motion and the motion of an object in a circle with a constant or uniform speed. If you have a uniform speed and circumference, then this allows you to calculate the average speed of object. Speed and Velocity have the same scalar velocity but they differ with magnitude because velocity has magnitude, while speed does not. Another difference between the two is that average velocity must include direction, and is always changing, while speed is not.
B - The Truth Behind Acceleration
Acceleration is equal to the change in velocity over the total amount of time. It can either have changing magnitude or direction. When an object is moving in circles at a constant speed they accelerate towards the center of the circle. The weight of the object also is a factor on whether the acceleration is greater or less. The lighter the objects the greater the acceleration, and this will cause it to lean in towards the acceleration.
C- There's always a requirement, even when talking about Centripetal Force!
When an object is in uniform circular motion, it experiences an inward net force, or it is sometimes called a centripetal force. The centripetal force is what alters the direction for the object. It allows the force to have the ability to alter the direction of the object's velocity vector without altering its magnitude. This is done by displacement. This force is directed perpendicular to the tangental force.
D -How does the Forbidden F-word relate to Physics?
Centrifugal force is a weird word, but it has an important meaning. It means away from the center or outward. Without this inward force, the circular motion would not exist.
E- So many Equations! Each representing so many different things!
To calculate average speed you use the circumference, divided by time. To find acceleration, it is (2) (PI) (R) squared all divided by time. The unbalanced force is always in the direction of the center of the circle. Acceleration is inversely proportional to the mass.
Lesson 2 12/22
Applications of Circular Motion (A-C) A. Newton's Second Law - Revisited
Circular Motion can be used in many different ways.
If you use the equations from Newton's second law, you can find a bunch of other variables, without using givens.
There isn't really a set formula when you are solving these types of problems, all you do is use what is given to you and work from there.
B. Roller Coasters and Amusement Park Physics
On many roller coasters, there is either a loop or a hill.
These rides involve max and min speed, as well as finding acceleration to determine the safety.
Clothoid loops are when the centripetal acceleration is inside.
The radius at the bottom of this type of loop is larger than the radius at the top.
C. Athletics
Circule motion can be found in almost every sport.
The most popular example of it is a turn.
Contact Force supplies two roles
1) balances the downward force of gravity
2) meets the centripetal force requirement for an object in uniform circular motion.
Circular Motion is the inward acceleration and it is caused by an inward net force.
Lesson 3 1/3
Universal Gravitation (A-E) A. Gravity is more than a Name
Gravity is a very unique force in a way that it is involved and present almost everywhere.
Surprisingly the acceleration and force of gravity are different.
Gravity is not effected by mass.
Gravity can either increase acceleration, or decrease acceleration.
B. The Apple, the Moon, and the Inverse Square Law
Kepler's 3 Laws of Planetary Motion
Law of Ellipses: the paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus.
Law of Equal Areas: an imaginary line drawn from the center of the sun to the center of the planet and it will sweep out equal areas in equal intervals of time.
Law of Harmonies: ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances form the sun.
Circular Motion
not linear
requires a centripetal force
Newton
Discovered the notion of Universal Gravitation
Relates to the motion of the Earth
He used the inverse square law, which states that the relationship between the force of gravity between the earth and any other object and the distance that separates the two centers can be described as Fg : 1 d2
C. Newton's Law of Universal Gravitation
Equation: Fg = G m1 X m2 / d2
G is a constant (6.67 X 10 ^ -11)
As the mass of either object increases, the force of gravitational attraction between them all increases.
Universality = the concept that all objects attract each other with a force of gravitational attraction
Gravity is universal
The Gravitational force is directly proportional to the mass of both interacting objects.
Perturbation = tendency to deviate from its otherwise smooth path.
D. Cavendish and the Value of G
It explains the forces between two objects that makes them rotate.
G is small
He discovered the value of G by using a torsion balance.
E. The Value of g
g = acceleration of gravity
9.8 m/s2
The acceleration go gravity of an object can be measures
This value is independent of the mass of the object and only dependent upon location.
The Clockwork Universe 1/5
1-4 Part 1
The term heliocentric refers the the sun as the center of the solar system.
Copernicus was the one who first proposed this, and even though he turned out to be right his ideas were not widely spread as much as others were.
After Copernicus died, Galileo was technically forced into following his ideas and researching them more.
Keplerian System
In this system, a planet follows an elliptical orbit
At the same time, the sun is at one focus of the ellipse.
Part 2
Math was also involved during this time, thanks to an important mathematician Renes Descartes who discovered many equations.
They linked algebra and geometry on the coordinate system.
Descartes supported Kepler's ideas
Part 3
Newton looks further into finding an explanation for Kepler's plan
To explain these theories that he had, Newton created laws.
He had 3 main points
Deviation from Steady Motion
Looked for a cause
Law of universal gravitation (no matter what two objects, ever object follows the same pattern)
Part 4
Newton only created one law about gravity
He combined what he already had to show the elliptical orbit of a planet around the sun.
Mechanics = the study of force and motion
Doctrine of free will = asserts that human beings are free to demonstrate their own actions.
Lesson 4 1/6
Circular and Satellite Motion (A-C) A. Kepler's Three Laws
1st Law
Explains that planets are orbiting the sun in a path described as an ellipse.
An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points are constant.
Other two points are foci
All planets orbit the sun in a path that is like an ellipse
2nd Law
Describes the speed at which any given planet will move while orbiting the sun
Speed is constantly changing
A planet moves fastest when it is closest to the sun and slowest when it's further
The law of equal areas shows the triangles that make up points of a circle.
3rd Law
This law compares the orbital period and the radius of orbit of a planet to those of other planets.
Studies the different motion characteristics of different planets.
B. Circular Motion Principles for Satellites
A satellite is any object that is orbiting the earth, sun, or other massive body and it can be natural or man made.
The moon is a natural satellite
Satellites act in a similar motion to projectiles because gravity is the only force affecting it.
The motion of satellites can be described by acceleration and velocity.
Satellites encounter inward forces and accelerations and tangential velocities.
There still is one, even when you're moving in an elliptical motion
C. Mathematics of Satellite Motion
The mass of projectiles has no affect upon the acceleration towards the earth and the speed at any point.
When only gravity is present, the mass of the moving object becomes a non-factor.
The only thing that radius is dependent on is the period, speed, and acceleration of a satellite.
D. Weightlessness in Orbit
When people feel weightless it is because there is no external force pushing or pulling upon their body
Action at a distance force:
can't be felt
Contact forces = touching whatever is being acted upon
One characteristic of circular motion is inward acceleration.
E. Energy Relationships for Satellites
Orbits of satellites can be described as either circular or elliptical
The speed of a satellite in an elliptical motion is constantly changing
as it moves closer to the earth it increases and as it moves further it decreases
Work-energy bar chart
represents the energy of an object by means of vertical bar
The work energy theorem and newton's laws apply to both the objects on Earth and the motion of the satellites.
toc Lesson 1 12/13
Lesson 2 12/22
Lesson 3 1/3
The Clockwork Universe 1/5
Lesson 4 1/6
Motion Characteristics for Circular Motion (A-E)Table of Contents
A - Circular Motion and Speed
- Circular Motion has many different forms. Consisting of uniform constant motion and the motion of an object in a circle with a constant or uniform speed. If you have a uniform speed and circumference, then this allows you to calculate the average speed of object. Speed and Velocity have the same scalar velocity but they differ with magnitude because velocity has magnitude, while speed does not. Another difference between the two is that average velocity must include direction, and is always changing, while speed is not.
B - The Truth Behind Acceleration- Acceleration is equal to the change in velocity over the total amount of time. It can either have changing magnitude or direction. When an object is moving in circles at a constant speed they accelerate towards the center of the circle. The weight of the object also is a factor on whether the acceleration is greater or less. The lighter the objects the greater the acceleration, and this will cause it to lean in towards the acceleration.
C- There's always a requirement, even when talking about Centripetal Force!- When an object is in uniform circular motion, it experiences an inward net force, or it is sometimes called a centripetal force. The centripetal force is what alters the direction for the object. It allows the force to have the ability to alter the direction of the object's velocity vector without altering its magnitude. This is done by displacement. This force is directed perpendicular to the tangental force.
D - How does the Forbidden F-word relate to Physics?- Centrifugal force is a weird word, but it has an important meaning. It means away from the center or outward. Without this inward force, the circular motion would not exist.
E- So many Equations! Each representing so many different things!Lesson 2 12/22
Applications of Circular Motion (A-C)A. Newton's Second Law - Revisited
- Circular Motion can be used in many different ways.
- If you use the equations from Newton's second law, you can find a bunch of other variables, without using givens.
- There isn't really a set formula when you are solving these types of problems, all you do is use what is given to you and work from there.
B. Roller Coasters and Amusement Park Physics- On many roller coasters, there is either a loop or a hill.
- These rides involve max and min speed, as well as finding acceleration to determine the safety.
- Clothoid loops are when the centripetal acceleration is inside.
- The radius at the bottom of this type of loop is larger than the radius at the top.
C. AthleticsLesson 3 1/3
Universal Gravitation (A-E)A. Gravity is more than a Name
- Gravity is a very unique force in a way that it is involved and present almost everywhere.
- Surprisingly the acceleration and force of gravity are different.
- Gravity is not effected by mass.
- Gravity can either increase acceleration, or decrease acceleration.
B. The Apple, the Moon, and the Inverse Square Law- Kepler's 3 Laws of Planetary Motion
- Law of Ellipses: the paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus.
- Law of Equal Areas: an imaginary line drawn from the center of the sun to the center of the planet and it will sweep out equal areas in equal intervals of time.
- Law of Harmonies: ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances form the sun.
- Circular Motion
- not linear
- requires a centripetal force
- Newton
- Discovered the notion of Universal Gravitation
- Relates to the motion of the Earth
- He used the inverse square law, which states that the relationship between the force of gravity between the earth and any other object and the distance that separates the two centers can be described as Fg : 1 d2
C. Newton's Law of Universal Gravitation- Equation: Fg = G m1 X m2 / d2
- G is a constant (6.67 X 10 ^ -11)
- As the mass of either object increases, the force of gravitational attraction between them all increases.
- Universality = the concept that all objects attract each other with a force of gravitational attraction
- Gravity is universal
- The Gravitational force is directly proportional to the mass of both interacting objects.
- Perturbation = tendency to deviate from its otherwise smooth path.
D. Cavendish and the Value of G- It explains the forces between two objects that makes them rotate.
- G is small
- He discovered the value of G by using a torsion balance.
E. The Value of gThe Clockwork Universe 1/5
1-4Part 1
- The term heliocentric refers the the sun as the center of the solar system.
- Copernicus was the one who first proposed this, and even though he turned out to be right his ideas were not widely spread as much as others were.
- After Copernicus died, Galileo was technically forced into following his ideas and researching them more.
- Keplerian System
- In this system, a planet follows an elliptical orbit
- At the same time, the sun is at one focus of the ellipse.
Part 2- Math was also involved during this time, thanks to an important mathematician Renes Descartes who discovered many equations.
- They linked algebra and geometry on the coordinate system.
- Descartes supported Kepler's ideas
Part 3- Newton looks further into finding an explanation for Kepler's plan
- To explain these theories that he had, Newton created laws.
- He had 3 main points
- Deviation from Steady Motion
- Looked for a cause
- Law of universal gravitation (no matter what two objects, ever object follows the same pattern)
Part 4Lesson 4 1/6
Circular and Satellite Motion (A-C)A. Kepler's Three Laws
- 1st Law
- Explains that planets are orbiting the sun in a path described as an ellipse.
- An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points are constant.
- Other two points are foci
- All planets orbit the sun in a path that is like an ellipse
- 2nd Law
- Describes the speed at which any given planet will move while orbiting the sun
- Speed is constantly changing
- A planet moves fastest when it is closest to the sun and slowest when it's further
- The law of equal areas shows the triangles that make up points of a circle.
- 3rd Law
- This law compares the orbital period and the radius of orbit of a planet to those of other planets.
- Studies the different motion characteristics of different planets.
B. Circular Motion Principles for Satellites- A satellite is any object that is orbiting the earth, sun, or other massive body and it can be natural or man made.
- The moon is a natural satellite
- Satellites act in a similar motion to projectiles because gravity is the only force affecting it.
- The motion of satellites can be described by acceleration and velocity.
- Satellites encounter inward forces and accelerations and tangential velocities.
- There still is one, even when you're moving in an elliptical motion
C. Mathematics of Satellite Motion- The mass of projectiles has no affect upon the acceleration towards the earth and the speed at any point.
- When only gravity is present, the mass of the moving object becomes a non-factor.
- The only thing that radius is dependent on is the period, speed, and acceleration of a satellite.
D. Weightlessness in Orbit- When people feel weightless it is because there is no external force pushing or pulling upon their body
- Action at a distance force:
- can't be felt
- Contact forces = touching whatever is being acted upon
- One characteristic of circular motion is inward acceleration.
E. Energy Relationships for Satellites